n-bridge braids and the braid index

2022/08/29 by Gollero, Dane, Krishna, Siddhi, Loving, Marissa +3
#57K10 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2208.13655

Abstract

In this work, we find a closed form formula for the braid index of an n-bridge braid, a class of positive braid knots which simultaneously generalizes torus knots, 1-bridge braids, and twisted torus knots. Our proof is elementary, effective, and self-contained, and partially recovers work of Birman--Kofman. Along the way, we show that the disparate definitions of twisted torus knots in the literature agree.

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